Induced Eddy Currents in Simple Conductive Geometries: Mathematical Formalism Describes the Excitation of Electrical Eddy Currents in a Time-Varying Magnetic Field
In this paper, a complete mathematical formalism is introduced to describe the excitation of electrical eddy currents due to a time-varying magnetic field. The process works by applying a quasistatic approximation to Ampere's law and then segregating the magnetic field into impressed and induced terms. The result is a nonhomogeneous vector Helmholtz equation that can be analytically solved for many practical geometries. Four demonstration cases are then solved under a constant excitation field over all space—an infinite slab in one dimension, a longitudinal cylinder in two dimensions, a transverse cylinder in two dimensions, and a sphere in three dimensions. Numerical simulations are also performed in parallel with analytic computations, all of which verify the accuracy of the derived expressions.
- Research Organization:
- Univ. of Utah, Salt Lake City, UT (United States)
- Sponsoring Organization:
- USDOE Advanced Research Projects Agency - Energy (ARPA-E)
- Grant/Contract Number:
- AR0000411
- OSTI ID:
- 1433514
- Journal Information:
- IEEE Antennas and Propagation Magazine, Vol. 60, Issue 1; ISSN 1045-9243
- Publisher:
- IEEECopyright Statement
- Country of Publication:
- United States
- Language:
- English
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